Just an experiment - it's on the short side and the sounds might not be the best, but just wanted to try it out. If anyone is interested in this kind of video I can try making a better quality one soon. Should have some others coming the next few days :)
To listen while using other apps, switch the player to Picture-in-Picture (PiP) during playback — it keeps playing in a small floating window (the screen stays on).
To listen with the screen fully off, in-browser playback stops by YouTube's design. Open the video in the YouTube app to keep listening where background playback is supported (e.g. with YouTube Premium).
Open in YouTube app